class_docstr: Calculates the Geometric Mean Relative Absolute Error.
  
  .. math::
      \text{GMRAE} = \exp(\frac{1}{n}\sum_{j=1}^n \ln\frac{|A_j - P_j|}{|A_j - \bar{A}|})
  
  where :math:`A_j` is the ground truth, :math:`P_j` is the predicted value
  and :math: `bar{A}` is the mean of the ground truth.
  
  More details can be found in `Botchkarev 2018`__.
  
  - ``update`` must receive output of the form ``(y_pred, y)`` or ``{'y_pred': y_pred, 'y': y}``.
  - `y` and `y_pred` must be of same shape `(N, )` or `(N, 1)`.
  
  __ https://arxiv.org/abs/1809.03006
  
  Parameters are inherited from ``Metric.__init__``.
  
  .. warning::
  
      Current implementation of GMRAE stores all input data (output and target)
      as tensors before computing the metric.
      This can potentially lead to a memory error if the input data is larger than available RAM.
  
      In distributed configuration, all stored data (output and target) is mutually collected across all processes
      using all gather collective operation. This can potentially lead to a memory error.
  
      Compute method compute the metric on zero rank process only and final result is broadcasted to
      all processes.
  
  Args:
      output_transform: a callable that is used to transform the
          :class:`~ignite.engine.engine.Engine`'s ``process_function``'s output into the
          form expected by the metric. This can be useful if, for example, you have a multi-output model and
          you want to compute the metric with respect to one of the outputs.
          By default, metrics require the output as ``(y_pred, y)`` or ``{'y_pred': y_pred, 'y': y}``.
      device: specifies which device updates are accumulated on. Setting the
          metric's device to be the same as your ``update`` arguments ensures the ``update`` method is
          non-blocking. By default, CPU.
  
  Examples:
      To use with ``Engine`` and ``process_function``, simply attach the metric instance to the engine.
      The output of the engine's ``process_function`` needs to be in format of
      ``(y_pred, y)`` or ``{'y_pred': y_pred, 'y': y, ...}``.
  
      .. include:: defaults.rst
          :start-after: :orphan:
  
      .. testcode::
  
          metric = GeometricMeanRelativeAbsoluteError()
          metric.attach(default_evaluator, 'gmare')
          y_true = torch.tensor([0., 1., 2., 3., 4., 5.])
          y_pred = y_true * 0.75
          state = default_evaluator.run([[y_pred, y_true]])
          print(state.metrics['gmare'])
  
      .. testoutput::
  
          0.0...
code: def compute(self) -> float:
      if len(self._predictions) < 1 or len(self._targets) < 1:
          raise NotComputableError(
              "GeometricMeanRelativeAbsoluteError must have at least one example before it can be computed."
          )
  
      _prediction_tensor = torch.cat(self._predictions, dim=0)
      _target_tensor = torch.cat(self._targets, dim=0)
  
      # All gather across all processes
      _prediction_tensor = cast(
          torch.Tensor, idist.all_gather(_prediction_tensor)
      )
      _target_tensor = cast(
          torch.Tensor, idist.all_gather(_target_tensor)
      )
  
      result = torch.exp(
          torch.log(
              torch.abs(_target_tensor - _prediction_tensor)
              / torch.abs(_target_tensor - _target_tensor.mean())
          ).mean()
      ).item()
  
      return result
  
file_path: ignite/ignite/contrib/metrics/regression/geometric_mean_relative_absolute_error.py
imports: from typing import cast, List, Tuple
  import torch
  import ignite.distributed
  from ignite.contrib.metrics.regression._base import _BaseRegression
  from ignite.exceptions import NotComputableError
  from ignite.metrics.metric import reinit__is_reduced
label_desc: Use image node_id 3 for calling the GeometricMeanRelativeAbsoluteError obj's underlying member method code with example usage: obj.compute() and returns: result